[V. G. Karpov] from the University of Toledo suggest these whiskers are formed by differences in charge induced by metallurgical anomalies – contamination, differences in the grain of the solder, and oxides. Because of the difference in charge, the whiskers are extruded, for lack of a better word, out from the surface of the solder.

The theory of whisker growth is generally consistent with observed rates of whisker growth and other properties. With this theory, it should even be possible to grow tin whiskers. Why anyone would want to do that other than, ‘because it’s cool’ is anyone’s guess, but there you go.